The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for parallel MRI image reconstruction using digital beamforming that accounts for the directivity of transmit and receive radio frequency (“RF”) elements, such as RF coils or RF antennas, used to obtain magnetic resonance signals.
Parallel MRI (“pMRI”), together with the wider availability of high field MRI, promise to bring about major improvements in the sensitivity and specificity and open the door for numerous clinical applications. The introduction of pMRI has spurred interest in optimal beamforming, but much of the focus of the early work was on the use of multiple independent RF receiver coils. Methods like the root of sum of squares (“RSS”) were shown to provide acceptable performance. The argument was that combining the images as a sum-of-squares results in high SNR as long as at least one of array coils has high SNR with all the coils having similar noise. However, the problem of combining image pixels from arrays with different type of image artifacts remains a challenge.
Adaptive reconstruction of using phased arrays was described by D. O. Walsh, et al., in “Adaptive Reconstruction of Phased Array MR Imagery,” Magn Reson Med, 2000; 43(5): 682-690. Walsh presented several example reconstructions comparing the adaptive approach to RSS. The key advantages for adaptive reconstruction demonstrated by Walsh was the improvement of SNR in dark regions of the field-of-view and suppression of artifacts by adaptive nulling. The adaptive nulling was achieved by computing the noise covariance matrix from a region in the FOV where motion and/or flow artifacts are present. The adaptive approach finds an optimal complex vector, m, that is obtained from solving an eigenvalue problem for the matrix Rn−1Rs, where Rs and Rn are, respectively, the signal and noise correlation matrices. These matrices can be estimated on a pixel-by-pixel or regional basis, depending on the problem. In practice, the signal and noise correlation matrices are estimated using complex image (or noise calibration) data from the array coils in a specified region of interest,
                                                        R              ^                        ⁡                          (                              p                ,                q                            )                                =                                    ∑                                                (                                      x                    ,                    y                                    )                                ∈                ROI                                      ⁢                                                            C                  p                                ⁡                                  (                                      x                    ,                    y                                    )                                            ⁢                                                C                  q                  *                                ⁡                                  (                                      x                    ,                    y                                    )                                            ⁢                                                          ⁢              for              ⁢                                                          ⁢              p                                      ,                  q          =          1                ,        …        ⁢                                  ,                              n            c                    ;                                    (        1        )            
where Cp(x,y) is the complex image (or noise) data at pixel (x,y) formed by coil p, and nc is the number of coils. A common feature of the RSS and the adaptive methods relying on the complex data (noise) measurements is that the transmitter and receiver geometries are not explicitly used in image reconstruction. This can be seen as an advantage given that the radiation and reception patterns of the array elements can be complicated, especially with the subject present.